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Questions tagged [wolfram-alpha]

For mathematical questions related to the usage of Wolfram Alpha.

2
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0answers
55 views

Wrong Wolfram alpha result on $nth$ derivative?

I'm working with this function $$f(x)=\left(x+\sqrt{x^2-a}\right)^{-b}$$ and I would like to know the $nth$ derivative of $f(x)$. To this end, I ask Wolfram alpha about that given me the following ...
0
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1answer
34 views

Is there some technique to plot complex functions by hand?

Is there some technique to plot complex functions by hand? Particularly, consider e.g. $$x=\exp(t)\cos(t), y=\exp(t)\sin(t)$$ This is equivalent to $e^x(\cos(y)+i\sin(y))$ along line $y=x$, just ...
0
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0answers
30 views

Why do these Residues and Numerically Calculated Contour Integrals Disagree?

I've been trying to numerically approximate various contour integrals of the function $f(z)=\frac{\sin\left(\pi x\right)}{\sin^2\left(\frac{15\pi}{x}\right)}$, but it seems that the residues and ...
2
votes
1answer
92 views

A bug in Wolfram Alpha about an infinite series?

While verifying this MSE answer, I may have come across a bug in Wolfram Alpha. It evaluates the sum below as, $$\qquad A=\sum_{n=0}^\infty\frac{\binom{2n}{n}^2}{16^n(n+1)^3}=1.03928049\color{red}{51}...
-1
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0answers
19 views

What does meant ImagePeriodogram and what does meant in mathematics?

I have tried to get fourier transform of this function $ \exp(-x²\text{erf}(x)))$ using wolfram alpha from $x=1$ to $2$ also i didn't get any image from $0$ to $\infty $ I have got the below graph ...
0
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0answers
39 views

Plot a graph with a hole in Wolfram Alpha

I would like to emphasize graphs with holes in Wolfram alpha, so I've tried graphing a rational function with a hole. However, the graph that WA is generating isn't showing the hole. Is there a way to ...
0
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1answer
38 views

How does one plot $z=(-2)^{3/5}$?

How does one plot $z=(-2)^{3/5}$? I see in Wolfram Alpha: https://www.wolframalpha.com/input/?i=z%5E5%3D-8 But I don't understand how that plot is created.
1
vote
1answer
37 views

3D plot difference Matlab and Wolfram

I'm trying to plot the function $z = 6x^2 - 4x^2y^2$ in Matlab. The code I'm using for this in matlab is the one below, also the plot is shown: ...
2
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1answer
41 views

FFT from scilab is different than wolfram alpha [closed]

I am getting completely different values of FFT([1,2]) in scilab and Wolfram. I wondering what is going on and who is right. ...
0
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0answers
19 views

Numerical Double Integration with inverse over inner integral failing using common methods and inbuilt functions

Implementing a paper, I want the value of this double integral which has endpoint singularities in both integrals. $\int_0^{\inf} \frac{1}{w} Im( 0.5^{-iw}({12{\int_0^1 (1 - (0.5+\frac{0.5} {1+by^\...
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2answers
35 views

Why “is $f(x)$ an odd function?” does not work with this function?

We know that $f(x)$ is odd if $-f(x)=f(-x)$. The function is $$f(x)=\begin{cases}2x-1&\text{if $-2<x<0$},\\2x+1&\text{if $0\leq x\leq2$}.\end{cases}$$ (link) Now I want to know if $f$ ...
2
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2answers
42 views

Infinite sum and partial sum not equal in Wolframalpha

$$\sum_{n=0}^{\infty} |(-0.8)^n \theta(n)-(-0.8)^{n-1} \theta(n-1)|$$ $\theta(n) = 1$ for $n \geq 0$ and 0 otherwise. My attempt to calculate this summation numerically with Python yielded 10. To ...
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0answers
20 views

How to plot a Riemann sum in Wolfram alpha

I am wondering if there's a simple way to plot a function with a Riemann sum in Wolfram alpha. I've looked in a bunch of places for a tutorial but can't seem to find one. Anyone wanna help please?
0
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2answers
45 views

Is Wolfram Alpha wrong? (trig identity)

I have the following identity $$ \sqrt{\cos(2x)\sec^4(x)}$$ I use the property $ \sqrt{a} \sqrt{b} = \sqrt{ab} $ which then yields $$ \sqrt{\cos(2x)} \, \sec^2(x) $$ However, Wolfram tells me ...
0
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1answer
41 views

How to find coordinates that split this arc into 3 pieces of equal length?

I need the $x$ coordinates of two new points that split an elliptical arc between 2 given points in quadrant I into 3 equal pieces. How can I get these coordinates? I want to use Wolfram but I can ...
2
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1answer
49 views

Different forms of Maclaurin expansion of $f(x,y) = \frac{1}{x+y}$

I am trying to use Taylor series to approximate the value of $f(x,y) = \frac{1}{x+y}$ for some code I am writing. Using WolframAlpha to quickly compute the Maclaurin series gives me: $$ \frac{1}{y} - \...
0
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0answers
23 views

Calculating an area of parametric function with wolframalpha?

Using wolframalpha, how can I calculate an area between some parametric function like: $\begin{cases} x(t) = t^2 - t \\ y(t) = t^3\end{cases}$ and: some other function like: $y = x^2$ ? I've ...
0
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2answers
46 views

How to find $\frac{146}7 \mod{7}$?

I understand that if $\gcd{(b,c)}=1$ then we can find $\frac{a}b\mod{c}$ by writing $$x\equiv \frac{a}b\mod{c}$$ $$bx\equiv a\mod{c}$$ then reducing $a$ and solving the modular equation by finding the ...
2
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3answers
50 views

How to compute $a\cdot \lim\limits_{n \to \infty}n?$

How to compute $$a\cdot \lim_{n \to \infty}n?$$ I think such an expression is not valid. Though $\lim\limits_{n \to \infty}n=\infty$, which is not a concrete real number, we can not put it into a ...
3
votes
1answer
144 views

Why wolfram alpha claimed that this $\sum_{n=1}^{\infty}\sin (\frac{n}{\sqrt{n!}}) $ is converge by test and in the same time is diverge?

I'm confused why wolfram alpha claimed that this sum $$\sum_{n=1}^{\infty}\sin \left(\frac{n}{\sqrt{n!}}\right) $$ is convergent by test criterion, and in the same time is divergent in result below ...
6
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1answer
76 views

Inconsistency of limits

Let $I_n(x)$ and $L_n(x)$ be the modified Bessel and modified Struve functions of order $n$, respectively. Assuming $x$ is real, I am interested in the following limit: $$ \lim_{x\to\infty} \frac{I_0(...
0
votes
2answers
35 views

Ability to generate a list of 3-digit numbers from a pool of digits in Wolfram?

I am attempting to generate a list of all possible 3-digit numbers that can be made by the numbers 1, 3, 5, 6, 7 and 9. I believe Wolfram should have the ability to give me a list, however, I am not ...
1
vote
2answers
71 views

Integral in Symbolab and WolframAlpha have different results

So Wolfram Alpha and Symbolab have different reuslt for this integral $\int \frac{x}{x+2}dx$. I done it myself and got result like Wolfram Alpha : $x-2\ln|x+2|$. Symbolab display this one: $x+2-2\ln|x+...
2
votes
5answers
46 views

Range of function $f(x)=x \sqrt{1-x^2}$

How to find range of this function, it looks easy but somehow I am not able to do that . What is more important to me is , why is wolframalpha unable to find the range , is it not a simple enough ...
1
vote
2answers
69 views

Are all values of $x$ solutions for $e^{2\ln(\sin(x))} = 1 - e^{2\ln(\cos(x))}$ in $\mathbb R$?

Does all values of $x$ in $\mathbb R$ satisfy equation: $$e^{2\ln(\sin(x))} = 1 - e^{2\ln(\cos(x))}$$ I am asking this, because by checking WolframAlpha solution there is an answer: (all values for $...
0
votes
1answer
41 views

Solving simple quadratic - Wolfram Alpha confusion?

I have the following quadratic $$(2\sqrt 2 - 2)x^2 + \sqrt8 x + (1+\sqrt 2)=0$$ Now the discriminant of this is $0$, so it has one real repeated root. A plot on Desmos confirms this. However, ...
0
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3answers
59 views

Calculating Fourier series of $\cos^2(t)$ gives unexpected result

As I understand it: $\cos^2(t)$ is even because it is a product of two even functions $\cos(t)$. The Fourier series and Fourier cosine series of an even function is the same link. So in the fourier ...
3
votes
2answers
123 views

Solving $1^x+2^x+3^x=0$ equations…

Is it possible to solve for x this kind of equation? Since 1,2,3 are not multiples to each other I see a priori no possibility. $$1^x+2^x+3^x=0; x?$$ Computing this on Wolfram Alpha, for example, ...
0
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2answers
77 views

Simple Differential Equation in Matlab and Wolfram get two different answer?

I'm a beginner in using Matlab. if I have a DE like $$x'(t)=\frac{1}{\sin (2x)}$$ How I can Implement in Matlab to calculate just answer? I try dsolve like as: ySol(t) = dsolve(ode,cond) but ...
-1
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1answer
45 views

Wrong wolframalpha result, calculating Carmichael number?

I put to wolframalpha $3^{560}\pmod{561}$ and result should be $1$ ($561$ is Carmichael number), but result is $375.$ https://www.wolframalpha.com/input/?i=3%5E560mod561 Why this happens? I found ...
0
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1answer
45 views

How to make Wolfram Alpha give me a range of possible answers for an equation if the subject is assumed to be an integer?

I am trying to use Wolfram Alpha, and I am trying to get it to give me a range of possible answers for y=(391-x)/x, if y was an integer. However, there are two problems I face with this. The first is ...
0
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1answer
66 views

Prove that $\sum_{i=1}^n \frac{1}{\sqrt i} < 2 \sqrt n$ by induction - result doesn't match to wolfram alpha's result

According to wolfram alpha, this inequality isn't true for $n > 2$. My result says otherwise. Assuming that the inequality is true for $n+1$, $\sum_{i=1}^{n+1} \frac{1}{\sqrt i} < 2 \sqrt {n+1}...
0
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0answers
19 views

Wolfram Mathematica input form of conditional probability

I heard that the conditional probability form of Wolfram Mathematica is like this: Probability[x < 1 \[Conditioned] ....... However, what is Mathematica input form of double conditioned. For ...
0
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1answer
32 views

Wolfram Alpha - FourierParameters not working with discrete fourier transform

I am trying to calculate the discrete fourier transform using the signal processing convention. The documentation gives the followng example: ...
2
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0answers
99 views

How can I compute a fourier series with Wolfram alpha?

How can I compute the Fourier series of a function on a interval using Wolfram ? For example, the Fourier of $f(x)=x^2$ on $[0,2\pi]$ prolonged on $\mathbb R$ by $2\pi$ periodicity. For example, if I ...
0
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2answers
65 views

Is there supposed to be a difference between $x^{1/3}$ and $\sqrt[3]{x}$ ? (Wolfram Alpha shows different results)

Compare these two functions: plot $\sqrt[3]{x}$ and plot $x^{1/3}$ I understand how roots are ambiguous, and Wolfram Alpha apparently takes the principle root with the $x^{1/3}$ case and the real ...
3
votes
2answers
332 views

Can I conclude that $\lim_{x\to0^+}\frac{x^2}{e^{-\frac{1}{x^2}}\cos(\frac{1}{x^2})^2}$ is infinite or it doesn't exists?

$$\lim_{x\to0^+}\frac{x^2}{e^{-\frac{1}{x^2}}\cos(\frac{1}{x^2})^2}$$ My intuition is that the denominator goes to 0 faster and everything is non-negative, so the limit is positive infinity. I cant ...
0
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0answers
15 views

The first principal subresultant coefficient of two polynomials

Let $f=f(x), g=g(x) \in \mathbb{C}[x]$, with $\deg(f)=\deg(g)=n \geq 2$. Write $f=(x-a_1)\cdots(x-a_n)$ and $g=(x-b_1)\cdots(x-b_n)$, where $a_i,b_i \in \mathbb{C}$, $1 \leq i \leq n$. Let $\lambda,\...
0
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0answers
35 views

Computing subresultants in WolframAlpha

Let $f(x)=(x-a_1)(x-a_2)\cdots(x-a_m)$ and $g(x)=(x-a_{m+1})(x-a_{m+2})\cdots(x-a_n)$, where $m,n \in \mathbb{N}$, $m < n$, $a_i \in F$, $F$ is a field of characteristic zero (for example, $k \in \{...
3
votes
2answers
74 views

Calculating value of $\text{sinc}(x)$, WolframAlpha and MATLAB give two different answers.

I need to evaluate the following: $$\frac{2}{3}\text{sinc}\bigg(\frac{2\pi}{3}(n-4)\bigg)-\frac{1}{3}\text{sinc}\bigg(\frac{\pi}{3}(n-4)\bigg)$$ for $n=[0,...,8]$ I don't have the sinc function in ...
1
vote
1answer
51 views

What is the meaning of a limit as $e^{(n+1) \infty}$ in WolframAlpha?

I inputted the following into WolframAlpha: lim x to 0 of (cotx)/x^n And I got $$\lim_{x \rightarrow 0}{\frac{\cot{x}}{x^n}} = e^{(n+1) \infty}$$ What does ...
0
votes
2answers
69 views

If $q \neq 5$ or $k \neq 1$, do the following conditions follow?

This is a follow-up to MSE question #2998091. From that question, we were able to get the bounds $$\frac{q-1}{q(q+1)} = f(1) \leq f(k) < \frac{q-2}{q(q-1)}$$ and $$0 < f(q) \leq f(5) = \frac{(5^...
0
votes
0answers
61 views

How to generate interpolating polynomial using Newton formula for exponential function?

I am trying to find interpolating polynomial of $f(x) = e^{3x}$ and interpolation nodes $x_0=x_1=x_2 = 0\ and\ x_3 = x_4 = 1 $ with Newton's formula using Wolfram Alpha, but I am stuck with division ...
3
votes
1answer
93 views

Why does Wolfram Alpha give $\sum_{n=1}^{\infty}(e^i)^{n^2}\approx9.92988+1.76807i$?

When I input $$\sum_{n=1}^{\infty}(e^i)^{n^2}$$ in Wolfram Alpha, it gives me the result, $$\sum_{n=1}^{\infty}(e^i)^{n^2}\approx9.92988+1.76807i$$ I think this is wrong, but I do not understand why ...
1
vote
1answer
104 views

Global extrema for $\frac{(q^k-1)(q^{k+1}-2q^k+1)}{{q^k}(q-1)(q^{k+1}-1)}$?

Does the function $$\frac{(q^k-1)(q^{k+1}-2q^k+1)}{{q^k}(q-1)(q^{k+1}-1)}$$ have either a global minimum or a global maximum for $q \geq 5$ and $k \geq 1$? WolframAlpha is unable to find any. ...
0
votes
1answer
38 views

Wolfram Alpha: How to find inflections points of functions involving arbitrary real constants

One of the WA demos shows how to find the inflection points of the following function: $x+\sin(x)$. How would you ask WA to find the inflection points of functions like $x+\sin(ax)$ or $a+bx+\sin(cx)$...
4
votes
3answers
90 views

WolframAlpha and I don't agree on $( xy\sin y )/(3x^2+y^2)$ as $(x,y)\to(0,0)$

WolframAlpha claims that the following limit does not exist: $$ \lim_{(x,y)\to(0,0)} \frac{xy\sin{y}}{3x^2+y^2} $$ https://www.wolframalpha.com/input/?i=lim+(xysiny)%2F(3x%5E2%2By%5E2)+as+%7Bx-%3E0,+...
1
vote
0answers
107 views

Why is $x \in \emptyset$ considered undetermined by WolframAlpha?

In an exercise, I had to prove, that the following statement is true: $A\setminus B = A \cap \bar{B}$ The task itself was not hard to solve, but I immediately had the question, if this statement ...
0
votes
1answer
32 views

Induction proof into wolframalpha not working

I'm trying to write this into wolframalpha without luck. Anyone know how to check it in there?
2
votes
1answer
48 views

How to probably insert proof by induction in wolframalpha

I'm trying to get this into wolframalpha.com by doing the "prove by induction" command to check my results. However I'm not sure how to insert it.